Nonsmooth Calabi-Yau structures for algebras and coalgebras
Rings and Algebras
2025-03-21 v2 Algebraic Geometry
Algebraic Topology
K-Theory and Homology
Representation Theory
Abstract
We show that generalised Calabi-Yau dg (co)algebras are Koszul dual to generalised symmetric dg (co)algebras, without needing to assume any smoothness or properness hypotheses. Similarly, we show that Gorenstein and Frobenius are Koszul dual properties. As an application, we give a new characterisation of Poincar\'e duality spaces, which extends a theorem of F\'elix- Halperin-Thomas to the non-simply connected setting.
Cite
@article{arxiv.2502.12162,
title = {Nonsmooth Calabi-Yau structures for algebras and coalgebras},
author = {Matt Booth and Joseph Chuang and Andrey Lazarev},
journal= {arXiv preprint arXiv:2502.12162},
year = {2025}
}
Comments
53 pages. v2: exposition improved, new Remark 8.10. Submitted version